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Fast time‐explicit micro‐heterogeneous wave propagation
Author(s) -
Maier Roland,
Peterseim Daniel
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800294
Subject(s) - computation , homogenization (climate) , simplicity , spacetime , computer science , stability (learning theory) , context (archaeology) , algorithm , mathematics , physics , geology , biodiversity , ecology , paleontology , quantum mechanics , machine learning , biology
Using explicit time stepping schemes in the context of wave propagation is very popular due to simplicity and fast computations. However, stability can only be guaranteed if a so‐called CFL condition holds that bounds the time step size with respect to the spatial mesh size. This is a severe restriction in case of micro‐heterogeneous media where spatial finescale features need to be resolved. We show how numerical homogenization in space both reduces the number of degrees of freedom in space and weakens the time step restriction.